Rules (Exponents)
(xa)(xb) = xa+b
(xa)b = xab
xa = xa-b
xb
x0 = 1
x-a = 1
xa
Rules (Logs)
loga+logb = logab
logan = nloga
logsab = c
base exponent
ac = b
change of base
loga = loga
logb
Derivative of an exponential function · The rate of change (or derivative) of an exponential function is also exponential · F(x0 = x where the derivative and function are the same · _ is ~2.7182 … between 2.5 and 3, also known as e (euler’s #) · e is the derivative of itself, therefore meaning: the derivative of e is e · y=e à y’=e
Natural Exponential and Logarithmic Functions: Tuesday, April 26, 2011. By: Arlanna Pugh Overview: Today in class we had the opportunity to watch one of Gillian's favourite math movies (starring Daffy Duck). After viewing the short film we participated in a Derivative Activity with a partner where we had to determine which rules were suitable for each question and then had to solve it accordingly (4 questions total). In-Class Worksheet: Derivatives of the Natural Exponential and Logarithmic Functions Answers were taken up in class. In-Class Homework: Differentiating Exponential Functions Homework Both answers to the two questions were required to be checked by Gillian Question #1: Identify any local extrema for the function: y = (x^4)(e^x) Steps for solution:
Solve for the first derivative
Set the first derivative to 0
Solve for x
Sub x values into the original function and solve for y
Answer #1: Local Min at (0,0); Local Max at (-4, 4.7) Question #2: A motorcycle cost $10,000, but its value depreciates over time. The value can be modeled by: V(t) = 10000(e^-t/4), where V is the value of the motorcycle after t years.
Rate of Change Expression:
V'(t) = -2500 (e^-t/4)
Rate that the value of the motorcycle was depreciating at when purchased:
V'(0) = -2500 (e^-0/4); therefore -$2500/ year
When to sell bike when it is worth 1/4 of purchase price:
1/4 x $10000 = $2500 2500 = 10000(e^-t/4) t = 5.5 years Tonight's Homework:
Review Natural Exponential and Logarithmic Functions
Practice review questions will be handed out tomorrow
QUEST: Friday, April 29, 2011.
Talha Sadiq April 27, 2011 Work Period
Today was a work period and we got time in class to work on the practice quest and a review sheet on Exponential and Logarithmic Functions. The quest on this chapter is on Friday, April 29, 2011. Here are some links that would help you review for the test! Good Luck!
Logs and ExponentsEmily Brant
April 18,2011
Rules (Exponents)
(xa)(xb) = xa+b
(xa)b = xab
xa = xa-b
xb
x0 = 1
x-a = 1
xa
Rules (Logs)
loga+logb = logab
logan = nloga
logsab = c
base exponent
ac = b
change of base
loga = loga
logb
Derivative of an exponential function
· The rate of change (or derivative) of an exponential function is also exponential
· F(x0 = x where the derivative and function are the same
· _ is ~2.7182 … between 2.5 and 3, also known as e (euler’s #)
· e is the derivative of itself, therefore meaning: the derivative of e is e
· y=e à
y’=e
April 20th - The Natural Logarithm
By Moe Qureshi
For more info on the natural logarithm visit:
http://mathworld.wolfram.com/NaturalLogarithm.html
http://en.wikipedia.org/wiki/Natural_logarithm
Natural Exponential and Logarithmic Functions:
Tuesday, April 26, 2011.
By: Arlanna Pugh
Overview:
Today in class we had the opportunity to watch one of Gillian's favourite math movies (starring Daffy Duck). After viewing the short film we participated in a Derivative Activity with a partner where we had to determine which rules were suitable for each question and then had to solve it accordingly (4 questions total).
In-Class Worksheet: Derivatives of the Natural Exponential and Logarithmic Functions
Answers were taken up in class.
In-Class Homework: Differentiating Exponential Functions Homework
Both answers to the two questions were required to be checked by Gillian
Question #1: Identify any local extrema for the function: y = (x^4)(e^x)
Steps for solution:
- Solve for the first derivative
- Set the first derivative to 0
- Solve for x
- Sub x values into the original function and solve for y
Answer #1: Local Min at (0,0); Local Max at (-4, 4.7)Question #2: A motorcycle cost $10,000, but its value depreciates over time. The value can be modeled by: V(t) = 10000(e^-t/4), where V is the value of the motorcycle after t years.
- Rate of Change Expression:
V'(t) = -2500 (e^-t/4)- Rate that the value of the motorcycle was depreciating at when purchased:
V'(0) = -2500 (e^-0/4); therefore -$2500/ year- When to sell bike when it is worth 1/4 of purchase price:
1/4 x $10000 = $25002500 = 10000(e^-t/4)
t = 5.5 years
Tonight's Homework:
Talha Sadiq
April 27, 2011
Work Period
Today was a work period and we got time in class to work on the practice quest and a review sheet on Exponential and Logarithmic Functions. The quest on this chapter is on Friday, April 29, 2011. Here are some links that would help you review for the test! Good Luck!
http://www.themathpage.com/acalc/exponential.htm
http://www.web-formulas.com/Math_Formulas/Calculus_Derivatives_of_Exponential_and_Logarithmic_Functions.aspx
http://www.math.brown.edu/help/explog.html
Homework:
Complete the review sheet & practice quest! Review for the quest this friday!
Jane Yang
April 29, 2011
Today we had our Logs and Exponential functions Quest